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(a)
(b)
Distance
1
2
3
4
5
6
7
1
2
3
4
5
6
7
Point
reflector
Curve of
maximum convexity
(c)
Diffraction
migrated position
of event
Wavefront
Curve of
maximum
convexity
Reflection event on
seismic section
Fig. 4.31 Principles of diffraction migration. (a) Reflection paths from a point reflector. (b) Migration of individual reflection events back
to position of point reflector. (c) Use of wavefront chart and curve of maximum convexity to migrate a specific reflection event; the event is
tangential to the appropriate curve of maximum convexity, and the migrated position of the event is at the intersection of the wavefront
with the apex of the curve.
direct modelling of ray paths through hypothetical mod-
els of the ground, the geometry of the reflecting inter-
faces being adjusted iteratively to remove discrepancies
between observed and calculated reflection times.
Particularly in the case of seismic surveys over highly
complex subsurface structures, for example those en-
countered in the vicinity of salt domes and salt walls, this
ray trace migration method may be the only method capa-
ble of successfully migrating the seismic sections.
In order to migrate a seismic section accurately it
would be necessary to define fully the velocity field of
the ground; that is, to specify the value of velocity at all
points. In practice, for the purposes of migration, an es-
timate of the velocity field is made from prior analysis of
the non-migrated seismic section, together with infor-
mation from borehole logs where available. In spite of
this approximation, migration almost invariably leads to
major improvement in the seismic imaging of reflector
geometry.
Migration of seismic profile data is normally carried
out on CMP stacks, thus reducing the number of traces
to be migrated by a factor equal to the fold of the survey
and thereby reducing the computing time and associated
costs. Migration of stacked traces is based on the assump-
tion that the stacks closely resemble the form of individ-
ual traces recorded at zero offset and containing only
normal-incidence reflection events. This assumption is
clearly invalid in the case of recordings over a wide range
of offsets in areas of structural complexity. A better
approach is to migrate the individual seismic traces
(assembled into a series of profiles containing all traces
with a common offset), then to assemble the migrated
traces into CMP gathers and stacks. Such an approach is
not necessarily cost-effective in the case of high-fold
CMP surveys, and a compromise is to migrate subsets of
CMP stacks recorded over a narrow range of offset dis-
tances, and then produce a full CMP stack by summing
the migrated partial stacks after correction for normal
moveout. Procedures involving migration before final
stacking involve extra cost but can lead to significant
improvements in the migrated sections and to more
reliable stacking velocities.
 
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